This question is a new (to me) wrinkle on the old Special Relativity spaceship pseudo-paradox gedankens.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose you observe two spaceships motionless relative to you, side-by-side a mile apart.

First, a rifle is fired from one at a target on the other, the bullet hits the target. Now they speed up to 2000 mph. The rifle is fired again, hits the target. There are two ways to look at this.

In spaceships' inertial frame they're still holding still relative to one another. By Galilean relativity, naturally the bullet hits the target again.

From observer's point of view the rifle, and the bullet, have acquired momentum from their spaceship. The bullet therefore doesn't leave the spaceship at 90 degrees as before. Instead (suppose the bullet speed is inherently 2000 mph) it goes at a 45 degree angle ahead, at 2828 mph, and hits the target.

Ok, now use a laser instead of a rifle. And, the spaceships speed up to .99 c. Everything else unchanged.

In spaceships' inertial frame they're still holding still relative to one another. By special relativity, naturally the photons from the laser hit the target again.

From observer's point of view, since the target is still hit by the photons, the path they take appears angled ahead about 45 degrees. Of course speed is still c, so it appears to take longer to cross the intervening space, but that's immaterial.

The question is: can we say the photons emitted transversely from the laser on the speeding spaceship acquired momentum from it, just like the rifle bullet?

Full disclosure: this is a trick question!

This quote is from "On The Electrodynamics of Moving Bodies", A. Einstein, translated by W. Perrett and G.B. Jeffery from original paper: "Zur Elektrodynamik bewegter Korper", Annalen der Physik, 17, 1905. First published by Methuen and Company, Ltd, 1923. Wikipedia, BTW, has the same quote.

The second postulate: "... light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."

Note that it says the "velocity" is independent of emitter motion, not "speed".

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# I SR pseudo-paradox: photons affected by emitter

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